Yeah, Core 2 is more directly related to the Pentium M than the Pentium 4.
The Pentium M was basically a Pentium 3 core with some added features of the Pentium 4, but thankfully not the extremely long pipelines. The Pentium M actually performed very well against the Athlon XP, so much so that I remember reading a lot of posts hoping that Intel would release a desktop version (which would mean higher clock speed) and of course a desktop motherboard for it. There was only one or two motherboards released for the Pentium M and of course a desktop version of the Pentium M never appeared.
If Intel had released the Pentium M instead of the Pentium 4, Intel probably would not have lost their performance crown to AMD's Athlon XP. I was impressed how well the Pentium M 1.5GHz in my ThinkPad T40 performed compared to my Athlon XP 2600+ OCed to 2.3GHz.
Kudos to that little Israeli team that developed the Pentium M for the laptop market.